Tunable optical resonator for harmonic generation and parametric amplification



Aug. 17, 19( 3,201,799

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ENERGY SOURCE FIG. 2

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Aug. .17, 1985 G 0 nova 3,201,709

TUNABLE OPTICAL RESOiJATbR FOR HARMONIC GENERATION 2 Sheets-Sheet 2 ANDPARAMETRIC AMPLIFICATION Filed D80. 19, 1963 FIG. 5

ENERGY SOURCE Unite States Fascist 3,201,709 TUNAliLE OPTICAL RFSONATORFOR HARMONIC GET-JERATION AND PARAMETRIC AMPLlFlCA- TlON Gary D. Boyd,Murray Hill, N.J., nssignor to Bell Telephone Laboratories,Incorporated, New York, N.Y., a corporation of New York Filed Dec. 19,1963, Ser. No. 331,864 11 Claims. (Cl. 330-45) This invention relates'toresonators that are particularly adapted for use in parametricgenerators and amplifiers and in harmonic generators of electromagneticwaves at optical frequencies.

This application is a continuation-in-part of my copcnding applicationSerial No. 224,295, filed September 18, 1952 and now abandoned.

In the eopending United States patent application by I. A. Giorclmaineand D. A. Kleinman, Serial No. 158,267, filed December 11, 196i andassigned to applicant's assignee, there is disclosed the use ofnonlinear, birefringent crystals for the harmonic generation of coherentlight. By the proper choice of the direction of propagation of theapplied light through the crystal, one can satisfy the well-known Tienw-fl conditions and the harmonic light made to add cumulatively inappropriate phase, over an extended path length. The resulting output isthe harmonic of the input wave. It is a limitation of the structuredisclosed by Giordmaine and Kleinman, however, that only harmonics of afixed input frequency can be produced, there being no means for tuningthe device over a range of input frequencies.

in the copending United States application by A. Ashkin, Serial No.224,294, filed September 18, 1962, and assigned to applicant's assignee,there is disclosed an arrangement whereby traveling wave parametricamplification and oscillations are possible over a wide range offrequencies in a single structure. The Ashkin inverttion is based uponthe discovery that a nonlinear optical medium which exhibits adequatebirefringence can be made to satisfy the Tic-n or-fi conditions and whenthe medium is used as a parametric amplifier or oscillator, can be madetunable over a wide range of frequencies.

Despite the obvious advantages of the Ashkin device, optimum operationrequires that a plurality of pairs of planar, parallel mirrors beadjusted both as to angle and spacing. Since such adjustments aredifficult to make and to maintain, there are practical problems inherentin the Ashkin devices which limit their application.

I c P The present invention overcomes the above-mentioned shortcomingsin the prior art devices by using a spherically shaped nonlinear,birefringent material. This spherically shaped element, which isrotatable about its center, is located between a pair of partiallytransparent mirrors.

The mirror centers and the center of the sphere are aligned along acommon axis and the incident light projected upon the sphere along thiscommon axis.

The resonator is tuned by varying the distance between the mirrors.Because of its symmetry, the optical axis of the material can beoriented at any angle to the direction of propagation of the incidentwave without seriously affecting the tuning, thereby satisfying the Tienw- B condition without the need for any further extensive adjustment ofthe mirrors as was necessary heretofore. It is thus an advantage of thepresent invention that the cavity tuning adjustment and the optimum w-Badjustment pf v the birefringent material are to a large degreeindependent adjustments.

To minimize the critiealness associated with adjusting and maintainingthe proper spacing between mirrors the mirror spacing can beperiodically varied by vibrating one &6

of the mirrors. The vibration of one of the mirrors causes it to beswept through the proper tuning position at regular intervals.

This expedient can be used in those applications in which a pulsedoutput is useful since the etlect produced by vibrating one of themirrors is to pulse modulate the output signal. If a continuous waveoutput is required, on the other hand, the resonator should be mademechanically stable to with? n a wavelength in accordance with cur rentpractices.

In the first embodiment of the invention, a pair of curved mirrors areused. In a second illustrative embodiment of the invention, a pair ofplanar mirrors are used. While planar mirrors would appear to presentmore difliculties of adjustment than curved mirrors, it can be shownthat due to the presence of the spherical element, the planar mirrors,as viewed from within the sphere, behave as curved mirrors and, as such,their adjustment is subantially less critical tl an would be expected.

The region of stable, low-loss operation of the resonator is defined forboth etttbodirnents, the planar mirrors being considered as curvedmirrors of infinite radius.

These and other objects and advantages, the nature of the presentinvention, and its various features, will appear more fully uponconsideration of the various illustrative embodiments now to bedescribed in detail in connection wi h the accompanying drawings, inwhich:

FIG. 1 is a first embodiment of the invention using curved mirrors;

FIG. 2 illustrates a method of applying two parallel signals to theresonator illustrated in FIG. 1;

P16. 3 shows a periodic sequence of lenses that is the equivalent of theembodiment of FIG. 1;

FIG. 4 is a stability diagram for the resonator of FIG. 1; and

HO. 5 is a second embodiment of the invention using parallel, planarmirrors and including means for vibrating one of the mirrors.

Referring now to FIG. 1, there is shown a diagrammalic view of a firstembodiment of a resonator 10, in accordance with the invention, usingphysically curved mirrors 11 and 12. The mirrors have curved reflectingsurfaces 13 and 14, respectively, which are partially lighttransmissive. Both mirrors have a radius of curvature b and centerswhich lie along a line :c-x' which defines the resonator axis.

Located centrally within resonahr 10 is a sphere 15 of nonlinear,birefringent material such as, for example, IQDHKHfl-OQ having anoptical axis designed 0-0. The material, more generally. can be eitheruniaxial or biaxiah in which case axis 0-0 is one of the optical axes.Simiiarly, th material can be either negative birefringent or positivebirefringent. The precise properties of the material used would dependupon the application at hand. For purposes of parametric devices andharmonic generators, the only essential properties are non linearity andbirefringence.

Coherent energy from an energy source 16, such as an optical maser, isdirected upon sphere 15 through mirror 11. Preferably. the center ofsphere 15 is located along the resonator rats and the direction ofpropagation of the incident wave energy derived from source 16 iscoincident with the resonator axis.

Means are provided for rotating sphere 15 within resonator 10 in orderto adjust the angle between the (ptic axis and L": direction of wavepropagation. Such variations in angie are effected in order to satisfthe Tien w-fi conditions whenever the resonator is tuned to a ditlcrentfrequency.

To avoid unduly cluttering the figure, hu'l'zver, the mechanism forrotating sphere 15 is not shown. Typically. a clamping mechanism is usedand means are provided for rotating the sphere about the axis of theclamp and, about the center of the sphere.

The resonator itself is tuned by an axial translational movement of oneor both mirrors 11 and 12, which movement varies the distance betweenthe mirrors. As is pointed out in the above-mentioned Ashkinapplication, the resonator can be tuned to multiple resonance forparametric applications.

The embodiment of FIG. 1, shown with a single energy source 16, can beused as a parametric oscillator which, upon the application ofsufficient pumping energy at a given frequency, produces a signal waveand an idler wave whose frequencies and phase constants depend upon theorientation of the optic axis of the sphere 15. Alternatively, theembodiment of FIG. 1 can be used as a harmonic generator in which signalenergy at a given frequency induces harmonic frequency components insphere 15.

For parametric amplification, energy from a coherent signal source canbe applied to resonator 1t: subs-tantially parallel to the energy rem acoherent pumping source 21, in the manner shown in FIG. 2, by means of asemitransparcnt mirror 23 oriented at 45 degrees to the two sources.

It is known that confocal and nonconfocal curved mirror resonators haveregions of stability and instability. That is, the resonator exhibitslow losses only for certain prescribed ratios of mirror spacing tomirror curvature. For a thorough discussion of confocal resonators, seethe article by G. D. Boyd and H. Kogclnik entitled Generalized ConfocalResonator Theory published in the July 1962 issue of the Bell SystemTechnical Journal, pages 1347 to 1370. In the instant case, the addedfocusing effect of sphere 15 is also taken into consideration.

From elementary optics, a sphere is known to be a th ck lens whoseprincipal planes are located at the center of the sphere. As a resultthe sphere behaves as a. thin lens having a focal length 1 given bywhere n is the index of refraction of the sphere in the chosen directionfor the matching of phase velocities, and

b; is the radius of the sphere.

The reflecting mirrors have focal length 1: given by where b is theirradius of curvature.

To find the allowed regions of stability, a periodic sequence of lenses,illustrated in FIG. 2, is considered. This sequency of lenses, which isequivalent to the resonator of FIG. l, is analyzed in the mannerdescribed by Boyd and Kogelnik.

FIG. 4 is the resulting stability diagram obtained for the resonatorshown in FIG. 1. In FIG. 4 the distance Z is the same as the distance Iof FIG. 3 due to the fact that the principal planes of sphere 15coincide at its center. The crosshatched portions of the diagram are theunstable regions of the periodic sequence of lenses represented in FIG.4, and indicate that a wave applied to a resonator having the iu licateddimensions would be highly attenuated. That is, the resonator has highdiffraction losses.

The stable operating region, or region of low diifra ction losses, isdefined by the two uncrosshatched portions of FIG. 4. Experience hasshown, however, that operation within the region defined by Z n 1 E 1 isto be preferred. That is, Z is greater than b but less than bpi/n-l.

In practice, there are some slight diffraction losses in the arrangementof FIG. 1 as a result of reflections from the surface of sphere 15. If,for any particular application, these losses become excessive, theregion of the resonator between the mirrors can be filled with atransparent liquid whose index of refraction matches that of the sphere.Alternatively, the sphere can be coated with an anti-reflection coatingusing any of the well-known thin film coating techniques.

The curved mirror arrangement of FIG. 1 has the disadvantage that theinput mirror, because of its curved shape, tends to detocus the incidentlight. A flat mirror, having parallel sides, on the other hand, wouldnot have this defocusing etl'ect and would, accordingly, be pre- Ierred.

FIG. 5 shows an alternate embodiment of the invention using parallel,planar mirrors instead of th curved mirrors used in the embodiment ofFIG. 1. As before, a sphere 52 is centrally located between the mirrors5t) and 51 with its center located along the axis of the reso nator.And, as before, the incident light is applied to sphere 52 along thisaxis.

In all essential respects the embodiment of FIG. 5 is the same as theembodiment of FIG. 1. In fact, the embodiment of FIG. 5 can beconsidered a special case of the embodiment of FIG. 1. That is, mirrors50 and 51 can be considered as curved mirrors of infinite radius. (i.e.,1)::00). It is included here as a separate embodiment because parallel,piarrar mirrors heretofore have been considered ditlicult to adjust.However, due to the focusing effect of sphere 52, the planar mirrors, asviewed from within the sphere, behave as curved mirrors and, as such,their adjustment is in tact substantially less critical than might beexpected. This can be readily seen to be so by considering thecombination of sphere 52 and each of the mirrors as a thick mirror inthe manner described on page 89 of Fundamentals of Optics by F. A.Jenkins and H. E. White, third edition, McGraw- Hill Book Company, Inc.considered, the parallel, planar resonator of FIG. 5 can be shown to bethe equivalent of a curved mirror resonator when viewed from withinsphere 52, and to havethe same adjustment characteristics of a curvedmirror resonator.

To further reduce the difficulties associated with adjusting andmaintaining the proper mirror spacing (resonator tuning), the distancebetween mirrors can be varied periodically in the manner described byDonald R. Herriott in an article entitled Spherical-lttirror OscillatingInterferometer" published in the August 1963 issue of Applied Optics,pages 855 and 866. As described by Herriott, one of the mirrors 51 inFIG. 5 is mounted so that it is free to move only in an axial direction.A coil 53 wound on one end of the mirror structure 54 is positioned inthe annular gap ofa permanent magnet 56 so that a current in the coil 53produces an axial force which moves the mirror 51 in the manner similarto a dynamic loudspeaker. Thus, a sinusoidal current applied to the coil53 from a source 55 causes an axial oscillator of mirror 51 which sweepsthe mirror through the proper tuning location at regular intervals.While this adds a modulation component to the resonator output, thisexpedient can nevertheless be used in those situations in which a pulsedoutput is preferred or can be tolerated.

The stability diagram for the planar mirror resonator shown in FIG. 5 isalso given by FIG. 4. However, recognizing that b is very large, thepractical tuning region is given by Though described in connection withthe embodiment of FIG. 5, it is understood that the technique ofvibrating one of the resonator mirrors can also be ap lied to theembodiment of FIG. I as well.

It is understood that the above-described arrangements are illustrativeof but a small number of the many possible specific embodiments whichcan represent applications of the principles of the invention. Numerousand varied other arrangements can readily be devised in accordance withthese principles by those skilled in the art without departing from thespirit and scope of the invention.

What is claimed is:

1. A tunable resonator comprising:

a patT'arairved, partially transparent mirrors of given radius ofcurvature whose centers of curvature lie along a common axis;

a nonlinear birefringent crystal of spherical shape having agive'iiiadius-disposed between said mirrors with its center along saidaxis;

said crystal having at least one optical axis;

means for rotating said sphere about its center for varying the anglebetween its optical axis and said common axis;

means for applying an electromagnetic wave to said crystal through oneof said mirrors;

and means for adjusting the distance between said mirrorsfortunin'g'said resonator within its stable region of operation asdefined by the ratio of the radius of curvature of said mirrors to theradius of said sphere.

2. The resonator according to claim 1 wherein said wave energy isapplied to said crystal at a given frequency; and including means forextracting wave energy from said cavity at twice said frequency.

3. T he resonator according to claim 1 wherein said 0 wave energy isapplied to said crystal at a signal frequency; means for applyingpumping wave energy to said crystal in a direction parallel to saidsignal wave;

and means for extracting amplified signal energy from said cavity. 4.The resonator as claimed claim 1 wherein the said ratio is greater thanunity but less than n/n-l.

5. The resonator as claimed in claim 1 wherein the direction ofpropagation of said wave is along said common axis.

6. The combination as claimed in claim 3 wherein the resonator is filledwith a material having an index of refraction equal to that of saidcrystal.

7. The resonator according to claim 1 wherein the radius of curvature ofsaid mirrors is infinite.

8. The resonator according to claim 1 including means for periodicallyvarying the distance between said mirrors.

9. A tunable resonator comprising: a pair of planar, partiallytransparent mirrors; a sphere of nonlinear, birefringent material havinga given radius centrally located between said mirrors; means forrotating said sphere about its center;

means for applying an electromagnetic wave to said a No referencescited.

ROY LAKE, Primary Examiner.

1. A TUNABLE RESONATOR COMPRISING: A PAIR OF CURVED, PARTIALLYTRANSPARENT MIRRORS OF GIVEN RADIUS OF CURVATURE WHOSE CENTERS OFCURVATURE LIE ALONG A COMMON AXIS; A NONLINEAR BIREFRINGENT CRYSTAL OFSPHERICAL SHAPE HAVING A GIVEN RADIUS DISPOSED BETWEEN SAID MIRRORS WITHITS CENTER ALONG SAID AXIS; SAID CRYSTAL HAVING AT LEAST ONE OPTICALAXIS; MEANS FOR ROTATING SAID SPHERE ABOUT ITS CENTER FOR VARY-